Pré-Publication, Document De Travail Année : 2024

Solving moment and polynomial optimization problems on Sobolev spaces

Résumé

Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares hierarchy, allowing to numerically solve non-convex polynomial optimization problems on infinite-dimensional Sobolev spaces with global convergence guarantees
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Dates et versions

hal-04393205 , version 1 (14-01-2024)
hal-04393205 , version 2 (15-11-2024)
hal-04393205 , version 3 (22-02-2025)

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Didier Henrion, Alessandro Rudi. Solving moment and polynomial optimization problems on Sobolev spaces. 2025. ⟨hal-04393205v3⟩
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